Non-equilibrium thermodynamics analysis of rotating counterflow superfluid turbulence

In two previous papers two evolution equations for the vortex line density $L$, proposed by Vinen, were generalized to rotating superfluid turbulence and compared with each other. Here, the already generalized alternative Vinen equation is extended to the case in which counterflow and rotation are not collinear. Then, the obtained equation is considered from the viewpoint of non-equilibrium thermodynamics. According with this formalism, the compatibility between this evolution equation for $L$ and that one for the velocity of the superfluid component is studied. The compatibility condition requires the presence of a new term dependent on the anisotropy of the tangle, which indicates how the friction force depends on the rotation rate.Comment: 18 pages, 3 figure

A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from an integral formulation of the radiation condition at infinity. In this Letter, we implement a Fourier-Chebyschev collocation method and show that this approach reduce the computational cost significantly. As a consequence, we give numerical evidence of some convergence estimates available in literature and we study the robustness of the algorithm at low and mid-high frequencies

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented

Coupled normal fluid and superfluid profiles of turbulent helium II in channels

We perform fully coupled two--dimensional numerical simulations of plane channel helium II counterflows with vortex--line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three--dimensions. We focus on the coarse--grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser--induced fluorescence of metastable helium molecules.Comment: 26 pages, 8 Figures, accepted for publication in Phys. Rev.

Turing pattern formation in the Brusselator system with nonlinear diffusion

In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in 1D and 2D spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover we consider traveling patterning waves: when the domain size is large, the pattern forms sequentially and traveling wavefronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and through a matching procedure we construct the outer amplitude equation and the inner core solution.Comment: Physical Review E, 201

Complex singularities and PDEs

In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries

Ukrainian Rushnyky: Binding Amulets and Magical Talismans in the Modern Period

The traditional ritual use of rushnyky among the Eastern Slavs continued to flourish throughout the Soviet period, despite the Communist Party’s efforts to curtail what was dismissed as superstitious folkloric survivals in village life. The paper briefly examines use of the rushnyk in the traditional Ukrainian village setting, followed by close readings of a number of towels from the author’s collection. These include careful analysis of a funeral/memorial rushnyk from the mid-20th c. that functioned as a mimetic grave for a soldier lost on the front. Attention is paid to the curious politicization of the ritual towel in Ukraine not only in the Soviet period, but subsequently in independent Ukraine, particularly in the recent country-wide creation of a "Rushnyk of National Unity"—the stitching of an oversized towel as a means to symbolize the binding of the disparate (and often combative) regions of the newly independent nation. This and other examples cited demonstrate innovation in the use of ritual towels and how they are being employed in new contexts where they can play a symbolic (if no longer fully understood ritual/magic) role